The invention is based on a flow rate meter for measuring the mass of a flowing medium. A flow rate meter is already known (German Offenlegungsschrift 31 09 608 which is a priority document for U.S. Pat. No. 4,450,714), which however, has the disadvantage that in so-called burn-off of the hot wire there is relatively no heat dissipation at the terminal support points, because of the large surface area of the angle connection elements, so that in a burn-off operation the hot wire does not heat up sufficiently in the vicinity of these end support points to burn off deposits from its surface. In the burn-off operation, as known for instance from German Patent 28 45 662 which is a priority document for U.S. Pat. No. 4,299,124, the hot wire is heated from its normal operating temperature of 20.degree. C., for example, to approximately 1000.degree. C., so that deposits firmly adhering to the surface of each hot wire are burned off. Deposits on the hot wire cause an undesirable change in the characteristic curve of the air flow rate meter, so that removing these deposits from the hot wire assures exact measurement of the flow rate of the medium over a long service life.